Question

Construct each angle ${37.5}^{\circ }$, using ruler and compasses:

Answer 1

Steps of constructions :
Step 1: Construct a line segment of PQ
Step 2: Considering P as centre and any radius, construct an arc which intersects PQ at the point R.
Step 3: Considering R as centre and same radius construct an arc which intersects the previous arc at the point S
Step 4: Considering S as centre and same radius construct an arc which intersects the previous arc at the point T
Step 5: Considering T and S as centre and radius more than half of TS,construct arcs which intersect each other at the point U. Join the line PU which intersects the arc in step 4 at the point V.
Step 6:Considering V and S as centers and radius more than half of VS,construct arcs which intersect each other at the point W .Join the line PW and $\angle$WPQ = ${75}^{\circ }$
Step 7: Bisects the $\angle$WPQ.Therefore,we know that $\angle$ZPQ = ${37.5}^{\circ }$.